• What are our objectives?
• Why Jamaica Stock Exchange (JSE)
• Company’s Profile for Portfolio
• Methodology
• Analysis
• Conclusion
• References

An investor would like to invest in the JSE, we want to present a model of a diversified portfolio that optimizes returns given the share price movements of the market

Best performing stock market in the world for 2015 and again in 2019 by Bloomberg.

Wall street flew the Jamaican flag on Wall street.

Nasdaq to deliver tech to Nasdaq

• Bank of the Year 2013 and best FX trader in Jamaica
• Been in Jamaica for over 125 years
• Banking Services , Insurance, Investments, Mortgage etc.

• Primary cement and gypsum manufacturer & supplier Caribbean
• 60 year old company
• Current growth due to boom of the construction industry

• One of the Caribbean’s largest conglomerates
• Diversified companies in the Caribbean, Europe and North America.

Scotia Group Jamaica (Jan 2013 - Jan 2020)

Caribbean Cement Co. (Jan 2013 - Jan 2020)

Grace Kenedy Group (Jan 2013 - Jan 2020)

Portfolio Return:

\[R_p = w_1R_1+w_2R_2+...+w_nRn\]

Expected Return:

\[E(R_p) = w_1E(R_1)+w_2E(R_2)+...+w_nE(Rn)\]

Covariance:

\[\sigma^2(R_p)=E[(R_p-E(R_p))^2]\]

Standard Deviation (Risk):

\[\sigma(R_p)=(E[(R_p-E(R_p))^2])^{1/2}\]

The sequence of consecutive trials such that:

\[Pr\{X_{n}=j\mid X_{n-1}=i_{n-1}, \dots,X_0=i_o\}\] \[= Pr\{X_{n}=j\mid X_{n-1}=i_{n-1}\}~~~~~~~~\]

Where order of subscripts in \(P_{ij}\) below corresponds to the direction of transition \(i > j\)

\[Pr\{X_{n}=j\mid X_{n-1}=i\}=P_{ij}\]

ja_folio <- portfolio.spec(assets = colnames(ja_returns))
ja_folio  <- add.constraint(
  portfolio = ja_folio , 
  type = "box", 
  min = 0.05, 
  max = 0.65
)

ja_folio  <- add.constraint(
  portfolio = ja_folio , 
  type = "leverage", # "full_investment"
  min_sum = 0.99,  
  max_sum = 1.01
) 

Maximize the mean return with ROI

max_return <- add.objective(
  portfolio = ja_folio , 
  type = "return", 
  name = "mean"
) 

Optimize

opt_max_return <- optimize.portfolio(
  R = ja_returns, 
  portfolio = max_return, 
  optimize_method = "ROI",
  trace = TRUE
)

print(opt_max_return$data_summary)

## $first
##              SGJ CCC GK
## 2013-01-02 -0.13   0  0
## 
## $last
##             SGJ  CCC   GK
## 2020-01-13 2.23 1.82 1.02

print(opt_max_return$weights)

##  SGJ  CCC   GK 
## 0.05 0.31 0.65

min_var <- add.objective(
  portfolio = ja_folio , 
  type = "risk",
  name = "var"
)

Optimize.

Note that although var is the risk metric, StdDev is returned as an objective measure.

opt_min_var <- optimize.portfolio(
  R = ja_returns, 
  portfolio = min_var,
  optimize_method = "ROI",  
  trace = TRUE
)

print(opt_min_var$data_summary)

## $first
##              SGJ CCC GK
## 2013-01-02 -0.13   0  0
## 
## $last
##             SGJ  CCC   GK
## 2020-01-13 2.23 1.82 1.02

print(opt_min_var$weights)

##       SGJ       CCC        GK 
## 0.3595696 0.2492720 0.3811584

meansd_ef <- create.EfficientFrontier(
  R = ja_returns,
  portfolio = ja_folio ,
  type = "mean-sd",
  n.portfolios = 20,
)

• An investment of $2000 in an equally weighted portfolio (consisting of CCC, GK and SGJ shares) would result in a return of $9850.96 over a two year period

• Returns for the CCC from the acquired data revealed a return of 319% and 691% for the years 2013 and 2014 respectively (this is due to a boom in the construction industry)

• Fieser, E. (2015, December 24) It’s Jammin’: Jamaica’s Tiny Stock Market Conquers World in 2015, Retrieved from http://www.bloomberg.com/news/articles/2015-12-24/it-s-jammin-jamaica-s-tiny-stock-market-conquers-world-in-2015

• Jamaica Stock Exchange Market Data (2016, May 25), Retreived from https://www.jamstockex.com/market-data/summary/

• Davou Nyap Choji, Samuel Ngbebe Eduno, Gokum Titus Kassem, (2013) Markov Chain Model Application on Share Price Movement in Stock Market, Computer Engineering and Intelligence Systems , (Vol. 4, No.10).

• Ching, W. Ng, (2006) M.Markov Chains: Models, Algorithms and Applications.

Let’s pRactice